Mathematical Analysis of Fourier Expansion Using Gauss Partial Sum

摘要

Fourier series is one of major specific and standard series of periodic functions that can be found in a wide range of theoretical and practical applications. Despite the Fourier series is old but still brand new in their practical applications especially in the field of communications. The present paper is a new version of the mathematical analysis for such a series using the partial Gauss sum. The functions that will be discussed herein are uniformly continuous and periodic. It is important also that by studying extension of the Fourier series sum for periodic functions, this will be helpful for one to be able to extend Gauss partial sum. The theoretical implementation is proved by solving an example and the results seem to be acceptable.